Multi-fractal properties in volcano-inspired variable density round jets*

Geophysical flows appear over a large range of scales, with Reynolds and Richardson numbers occurring over several orders of magnitude. Jet flow of varying densities ejected vertically into a large ambient region are considered. Using particle image velocimetry, the velocity fields were measured for three different gases exhausting into air, specifically helium, air and argon. Experiments considered relatively low Reynolds numbers from approximately 1500 to 5500 with Richardson numbers near 0.001 in magnitude. These included a variety of flow responses, notably nearly laminar, turbulent and transitioning jet flows. The data are analyzed using multifractal framework. The multifractal spectrum showed the characteristics of the flow based on the evolution in the streamwise and wall-normal direction. The variation of the Holder exponent displays the asymmetry and intermittency of the flow. Entropy dimension is used to check the flow evolution with scales. Quadrant analysis based on the pointwise Holder exponent and streamwise velocity is achieved. Scale dependent behavior is considered by quantifying the influence of the scale interactions in terms of the pointwise Holder condition.